Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 3 min ago
PreprintarXiv licencearXiv

A smooth quintic surface with 85 lines and Picard number 43

  • Xun Yu
  • Zigang Zhu
Open at sourcePDFDOICite

Abstract

We construct a pencil of complex quintic surfaces with every smooth member containing exactly $85$ lines. We show that one smooth member has Picard number $43$ and by introducing the notion of a d-saturated lattice, we prove that its Néron--Severi group is generated by the lines and four conics. We also construct smooth quintic surfaces with $79$ lines, including examples with $24$ pairwise skew lines, and a smooth surface of degree $10$ with $356$ lines, including $112$ pairwise skew lines.

Related

  1. Equivariant compactifications of a unipotent group by a smooth projective horospherical variety of Picard number one
    Hyukmoon Choi
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. A Picard-Theoretic Brauer Object for Derived Smooth Manifolds
    Yimu Mao, Christopher Tropp
    arXivPreprintarXiv licenceFull textMathematical physicsarXiv
  3. Sharp anticanonical volume bounds for Gorenstein Fano fourfold of Picard number one
    Pinxian Bie, Zhengjie Yu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. The Picard number of fibred Mori dream surfaces
    Federico Fallucca, Roberto Pignatelli, Francesco Polizzi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Weighted projective spaces admitting ℚ-Gorenstein smoothings to Fano threefolds with Picard number one
    Jungkai Alfred Chen, Yongnam Lee
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{yu2026smooth,
  title = {{A smooth quintic surface with 85 lines and Picard number 43}},
  author = {Xun Yu and Zigang Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26862},
  eprint = {2609.26862},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26862},
}
RIS
TY  - UNPB
TI  - A smooth quintic surface with 85 lines and Picard number 43
AU  - Xun Yu
AU  - Zigang Zhu
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26862
UR  - https://arxiv.org/abs/2609.26862
AB  - We construct a pencil of complex quintic surfaces with every smooth member containing exactly $85$ lines. We show that one smooth member has Picard number $43$ and by introducing the notion of a d-saturated lattice, we prove that its Néron--Severi group is generated by the lines and four conics. We also construct smooth quintic surfaces with $79$ lines, including examples with $24$ pairwise skew lines, and a smooth surface of degree $10$ with $356$ lines, including $112$ pairwise skew lines.
ER  -